Economics > QUESTIONS & ANSWERS > Public Economics: Problem Set 6 Solutions Columbia UniversityECON W4465ps6_solutions (All)

Public Economics: Problem Set 6 Solutions Columbia UniversityECON W4465ps6_solutions

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Public Economics: Problem Set 6 Solutions Cameron LaPointz December 7, 2016 Problem 1 (a) The consumer faces the following problem of maximizing utility over consumption in periods 1 and 2 subjec... t to budget constraints for each period: max C1;C2 ( log(C1) + 10 11 log(C2)) s.t. C1 + s = 21; 000 s.t. C2 = (1 + r)s where s denotes savings and in this problem and we assume throughout the interest rate is r = 0:1. We can combine the two per-period budget constraints into a single intertemporal budget constraint by substituting out for savings: C1 + 1+ C2r = 21; 000. Substituting the intertemporal budget constraint into the utility function for C1, we get the unconstrained maximization problem: max C2 ( log 21; 000 − 1 + C2r! + 10 11 log(C2)) The FOC of the unconstrained problem is − 1 1 + r!21; 000 − 1C2=(1 + r) + 10 11!C12 = 0 Solving the FOC for consumption in period 2 we get C2∗ = $11; 000. From the period 2 budget constraint, this implies savings must be s∗ = 1+ C2r = $10; 000. For this amount of savings, from the period 1 budget constraint we find that consumption in period 1 is C∗ 1 = 21; 000 − s = $11; 000. The consumer evenly smooths consumption across the two periods, C1∗ = C2∗. (b) With a 5% tax on consumption in each period, the budget constraints in each period become: [Show More]

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